Roberto C. Bochicchio

On the definition of bond orders at correlated level

Most often bond orders have heuristically been defined. In this work we follow a rigorous theoretical procedure looking for an appropriate definition of this concept. The study points out the exchange part of the pair density as a suitable starting point to set up a bond order definition, while the definitions based on the fluctuation of electron populations should be restricted to noncorrelated state functions. Numerical calculations are reported to illustrate these conclusions.

On the density matrix of effectively unpaired electrons

This Letter describes the relationships between the density of effectively unpaired electrons and other tools as the cumulant of the second-order reduced density matrix and the statistical population analysis. A topological population analysis, based on the atoms in molecules (AIM) theory, is incorporated in to the framework of the density of effectively unpaired electrons. Numerical determinations are carried out within this analysis in several systems and the results are compared with those of a more traditional Mulliken approach.

On spin density and hole distribution relations: valence and free valence

Abstract The formalism of the average or mean number of particles in a many-body system is applied to the “hole” distribution of many-electron molecular systems. In this way we rigorously derive expressions for the atomic valence and free valence magnitudes. It is shown that spin densities and free valence are directly related to each other in the case of maximum information state functions like ROHF (restricted open-shell Hartree-Fock) and UHF (unrestricted Hartree-Fock). For the case of correlated CI-like expansions free valence is interpreted as a measure of the non-uniform character of the spin distribution even in the case of systems with zero total spin number. Ab initio calculations of some selected molecules are presented and discussed.

Quantum statistical nature of the chemical bond.: Part I. Theoretical framework of population analysis and application to SCF closed shell wavefunctions

Abstract It is well known that the reduced density operator of order q is the essential tool for describing the electronic distribution in many-electron extended systems such as crystalline and molecular systems. In the present work this operator was used to generate a rigorous and general model of population analysis for particles ( q =1), “pairons” ( q =2), or in a more general sense, q -ons. For all q , it is possible to define population analyses of linear and non-linear structures, with regard to the mathematical shape of the generating functional of the particular analysis. If q =1, one of the linear types of analysis is the Mulliken type which is derived from a different basis from the original derivation, and from the non-linear type the Armstrong, Perkins and Stewart type (APS ) may be derived rigorously from physical principles, thereby allowing generalization of these definitions to more sophisticated wavefunctions. We define, as a byproduct, the bond multiplicity or degree of bonding, and the active, inactive and gross or proper populations in atoms within this last type of analysis which we call the statistical population analysis (SPA), in order to make explicit its nature. Furthermore, we apply SPA to the SCF closed shell formalism for first-order ( q =1) and second-order ( q =2) distributions. The numerical results are presented.

Energy decompositions according to physical space partitioning schemes

This work describes simple decompositions of the energy of molecular systems according to schemes that partition the three-dimensional space. The components of those decompositions depend on one and two atomic domains thus providing a meaningful chemical information about the nature of different bondings among the atoms which compose the system. Our algorithms can be applied at any level of theory (correlated or uncorrelated wave functions). The results reported here, obtained at the Hartree-Fock level in selected molecules, show a good agreement with the chemical picture of molecules and require a low computational cost in comparison with other previously reported decompositions.

On the definition of the spin-free cumulant of the second-order reduced density matrix

This note deals with the appropriate definition for the spin-free cumulant of the second-order reduced density matrix. Our approach leads to a direct derivation of one of the proposals reported by Kutzelnigg and Mukherjee [J. Chem. Phys. 116, 4787 (2002)] and it points out its suitability.

Atomic valence in molecular systems

Abstract Atomic valence in molecular systems is described as a partitioning of the hole distribution, the complementary part of the particle distribution. In this scheme, valence splits into three contributions, related to electron spin density, nonuniform occupancy of orbitals (nonpairing terms) and exchange density (pairing terms), respectively, and whose importance depends on the nature of the state of the system. Calculations carried out for correlated CI and Hartree–Fock state functions in both Mulliken and topological AIM type partitionings as well as theoretical results show the suitability of this formulation for describing valence concepts.

Determination of Local Spins by Means of a Spin-Free Treatment.

This work describes a Mulliken-type partitioning of the expectation value of the spin-squared operator corresponding to an N-electron system. Our algorithms, which are based on a spin-free formulation, predict appropriate spins for the molecular fragments (at equilibrium geometries and at dissociation limits) and can be applied to any spin symmetry. Numerical determinations performed in selected closed- and open-shell systems at correlated level are reported. A comparison between these results and their counterpart ones arising from other alternative approaches is analyzed in detail.

A study of the partitioning of the first-order reduced density matrix according to the theory of atoms in molecules.

This work describes a simple spatial decomposition of the first-order reduced density matrix corresponding to an N-electron system into first-order density matrices, each of them associated to an atomic domain defined in the theory of atoms in molecules. A study of the representability of the density matrices arisen from this decomposition is reported and analyzed. An appropriate treatment of the eigenvectors of the matrices defined over atomic domains or over unions of these domains allows one to describe satisfactorily molecular properties and chemical bondings within a determined molecule and among its fragments. Numerical determinations, performed in selected molecules, confirm the reliability of our proposal.

Relationships between cumulant and spin-density matrices: application to the decomposition of spin.

This paper reports the derivation of a relationship between some elements of the cumulant matrix of the second-order reduced density matrix and the elements of the spin-density matrix. This relationship turns out to be very useful to determine local spins through the partitioning of the spin expectation value of an N-electron system. The procedure enables expression of both one- and two-center contributions only in terms of one-electron matrix elements, the elements of the spin-density matrix. We report numerical determinations of local spins in the Hilbert space of atomic orbitals in selected molecules and radicals in triplet and doublet states.